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- W2003755322 abstract "The distinguishing number of a graph G is the minimum number of colors for which there exists an assignment of colors to the vertices of G so that the group of color-preserving automorphisms of G consists only of the identity. It is shown, for the d-dimensional hypercubic graphs Hd, that D(Hd)=3 if d∈{2,3} and D(Hd)=2 if d⩾4. It is also shown that D(Hd2)=4 for d∈{2,3} and D(Hd2)=2 for d⩾4, where Hd2 denotes the square of the d-dimensional hypercube. This solves the distinguishing number for hypercubic graphs and their squares." @default.
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- W2003755322 date "2004-06-01" @default.
- W2003755322 modified "2023-10-16" @default.
- W2003755322 title "The distinguishing number of the hypercube" @default.
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- W2003755322 doi "https://doi.org/10.1016/j.disc.2003.11.018" @default.
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